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Rudiments of Geometry 360-MS1-2GELa
Wykład (WYK) Rok akademicki 2022/23

Informacje o zajęciach (wspólne dla wszystkich grup)

Liczba godzin: 30
Limit miejsc: (brak limitu)
Literatura:

1) M. Audin, Geometry, Springer Verlag, 2003

2) H.S.M. Coxeter, Introduction to geometry, Wiley & Sons, 1969

Efekty uczenia się:

Knows basic techniques of the analytical affine geometry; in particular: he can determine equations of a line, a plane, and of an arbitrary subspace characterized in terms of their geometrical position, can solve problems where the affine cross ratio is involved, can apply the Ceva and the Menelaos Theorem - exam.

Knows fundamental types of affine transformations and their analytical characterization, can characterize affine transformations determined by means of simple invariants - exam.

Knows fundamental systems of notions used to characterize Euclidean Geometry (orthogonality, equidistance); can characterize mutual position of spheres and subspaces. Can use inversion to translate problems of inversive (Moebius) geoemetry into the language of Euclidean Geometry and vice versa - exam.

Knows and can use (in simple cases) principles of classification of isometries of Euclidean Spaces - exam.

After completing the course student gets backgrounds enabling him to learn and develop classical geometry - observation of students activity.

Metody i kryteria oceniania:

Written exam. Students can obtain up to 10 points for each task. To pass the exam student must get at least 50% from the maximal score.

Zakres tematów:

Analytical, coordinate affine space. Partition ratio of a segment. Barycentric coordinate system. The Ceva and the Menelaos theorem. Dilatations and affine maps.

Metric affine space. Symmetries, homotheties, isometries.

Metody dydaktyczne:

Lectures, consultation, work on literature, discussions in groups.

Grupy zajęciowe

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Grupa Termin(y) Prowadzący Miejsca Akcje
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